Why should faculty care about diversity, equity and inclusion?

Sumi Pendakur and I recently published an article in the Notices of the American Mathematical Society entitled, “Advocating for Diversity and Inclusion in Faculty Hiring,” in which we offer some best practices for faculty searches. Though it was written for people in the mathematical sciences, the strategies and tactics we offer can be used by any faculty search committee.

We wanted to share with you a section of the paper that didn’t make it into the final printed version, due to space constraints. We both consider this section to be an important piece of the puzzle.

I’m going to label this missing text as “Section 0” because it comes before Section 1. (This text will probably make more sense if you read it in the context of the rest of the article.)

Section 0. Why should faculty care about diversity, equity and inclusion?

Ultimately, the degree to which our institutions are successful at increasing diversity, equity and inclusion depends on how our institutions and those connected to it see these things as vital to their mission (Smith, 2009; Taylor, Milem, Coleman, 2016). The more that we can articulate our own reasons for promoting diversity, the better we can share those with others and see how they are connected with the missions of our institutions.

One of the most important steps that departments can take to support diversity in faculty hiring is actually something that takes place long before the position is approved. That step is to come to a shared understanding as a department about what is meant by words like “diversity” and “inclusion” and how those things relate to the mission of the department. If your institution has a strong vision for diversity, that is always a good place to start. Coming up with a department diversity statement can be helpful, but written documents like these are helpful only as much as they are supported and enacted by individuals in the department.

There are many specific reasons why your department or institution might value diversity in the mathematical sciences. The following economic argument is cited by publications such as “Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future”: minority groups are increasing as a percentage of the U.S. population and if these groups are not well-represented in the STEM workforce, we will suffer from a shortage of innovators who will spur economic growth.

Another argument has to do with the quality of work that we produce as a discipline. Without a broad representation of people, we cannot be sure that our work in the mathematical sciences addresses all of the important issues that need to be addressed, or that we are addressing these issues having heard all of the voices that need to be heard. More equitable participation will increase the robustness of our discipline.
Leadership is a common educational goal at many institutions, and that can often be a way to connect the mission of the institution with diversity. In today’s global society, multicultural competence and awareness of the societal impacts of one’s work is an increasingly important component of being a leader.

The student success imperative is also tied to the vision of diversity held by the institution and the search committee. Recruitment, retention, and successful graduation of an increasingly diverse (racially, sexually, and socioeconomically) student body is directly impacted by multiple factors, including quality of faculty interaction and whether students see themselves reflected in the curriculum and in the faculty body. The powerful mentoring relationships of faculty of color and students of color are well-documented in the literature and contribute to the feeling of a welcoming and inclusive learning environment. In addition, critical mass of minoritized communities in both the student and faculty bodies reduces stereotype threat, thereby enhancing academic success.

Then, there are a whole range of arguments for diversity having to do with social justice. If your institution or department has a goal of graduating ethical people who contribute to society, one can make the argument that it is important for our students to understand their mathematical work in a historical context of exclusion and underrepresentation in the mathematical sciences in the U.S. Hiring faculty who have an understanding of the historical and sociological context of patterns of exclusion in our discipline and are able to integrate that knowledge into their teaching benefits ALL students.

If your department can find consensus around a set of arguments for diversity, equity and inclusion, it will be much more likely that its actions, including teaching practices, curricula, and faculty hiring practices, will support these outcomes. It will also make it less likely that a search committee will fall into the trap of making a false dichotomy between excellence and diversity; instead search committees will see that diversity is part of what it means to reach excellence by fulfilling its goals.

References mentioned in this excerpt:

Smith, Daryl. Diversity’s Promise for Higher Education: Making it Work. John Hopkins University Press, 2009.

Taylor, Teresa E., Jeffrey F. Milem, and Arthur F. Coleman (2016). Bridging the research to practice gap: Achieving mission-driven diversity and inclusion goals. New York,
NY: College Board. Available at https://www.aacu.org/node/16225.

Active Learning 2.0: Making it Inclusive

I’ve written several posts (1, 2, 3) about why active learning is a good thing. There is even growing evidence that some forms of active learning seem to raise student learning outcomes and make those outcomes more equitable at the same time.

All of that is great, but I believe strongly that active learning is not a magic bullet and can be implemented well or poorly. It can sometimes alienate students. A few years ago, I asked students to work in groups on a set of problems in complex analysis. I didn’t give any instructions on how to work well with each other and the problems were rather routine ones. That created a situation in which a student felt left behind in her group and she got discouraged. I tried to talk to her after class but it didn’t help and she dropped the class shortly after.  She said that she dropped the class because it didn’t fit into her schedule, but I still suspect that the group work experience had something to do with it.

In this post, I would like to argue that just using active learning is not enough. Because active learning requires students to be more engaged in their own learning and often involves more human-to-human interactions, we must pay attention to how those experiences support or diminish students’ sense of competence and belonging. I believe that in most cases, what’s needed is a little more care and planning in the use of active learning. I’ll try to illustrate that through some examples.

Example #1: Think-Pair-Share

A common active learning strategy is “think-pair-share“. Unfortunately, I often find that instructors skip the “think” step and skip to “pair and share.” And more generally, I find that most speakers/facilitators/instructors don’t give any (or sufficient) independent think time before asking participants/students to talk with one another.

In many situations, independent think time is so important because it gives time for people who process information in different ways to put together their thoughts before talking. Some people are great at “talking while thinking”: putting together their ideas while talking it out. It can work out well if you’re like this and you’re around other people who are similar–the process of building off of each others’ ideas mid-sentence is fun to watch. Unfortunately, I’m not one of those people. I prefer to have some time to think before I just start talking and I don’t like it when other people interrupt me when I’m talking.

By giving students independent think time before asking them to discuss, instructors can give students more equitable access to the opportunity to think. Students with learning differences, students whose first language is not English, students who are introverted will appreciate having more time to think before speaking. Even those students who like to “talk while thinking” will probably have more refined ideas to share before they start talking. Therefore, the independent think time makes discussions far more productive and less awkward.  I dislike those moments when I’m in a room of people and the speaker/instructor asks us to talk to each other and there’s this awkward period when people are trying to figure out what to say and who should start, etc.

Example #2: Personal Response Systems

Personal Response Systems (for example, clickers) are great because they allow students to get timely feedback on their learning. But, imagine what it might feel like if you constantly answer questions incorrectly in class and you don’t feel supported in improving. Sometimes these Personal Response Systems also allow the instructor to display a distribution of answers in real time in class and it can be demoralizing when you can see that you’re one of a few who got the problem wrong and everyone else got it right.

I’m not suggesting that we should avoid giving students critical feedback that helps them improve. Critical feedback is important, but so is the way in which it is conveyed. When students receive feedback on their learning, it is important that the feedback be accompanied with the instructor’s high expectations for all students and support and encouragement for all students to meet those goals.  (See the work of Yeager and others on “wise feedback.”)

Typically these “clicker questions” are multiple choice questions. When these questions are designed well, the distractors (incorrect choices) often exploit some common student misunderstanding. When discussing the answers to the incorrect questions, you can point out the aspects of the incorrect choices that are correct or ask for what situation/question the incorrect choice could be a correct answer. (Also see “my favorite no.”)

And, don’t forget to provide multiple ways for students to get help if they need it.

Example #3: Group work

I saved this topic for last because I think it’s tricky to do well. The rewards and risks that accompany it are great.

If you assign students to work in heterogeneous ability groups (i.e., creating groups in which struggling students work with “more capable” students), there is always the risk of the groupings themselves to discourage students. Students aren’t dumb–they know that we sometimes group them in this way. If you are struggling in the class and you see that you’re always the one in the group that is struggling, and you’re not really getting the support you need from your peers, you might begin to wonder whether you really belong in the group and the class.  Students also don’t know how to help each other, especially in math classes–their understanding of what it means to help someone else usually involves telling someone a procedure or answer without providing any of the rationale.

But even if you group students in other ways, because you can’t be in all places at all times in the classroom, there is always the risk that one of your groups has negative interactions that spoil the learning for the group, or worse, cause some students to feel marginalized or excluded.

The example that I mentioned at the top of the post suggests a second reason why group work can go badly. When you ask students to work together on a task that really doesn’t require multiple brains, then you’re setting students up for to compare themselves with each other to see who can do it faster/better, or to zone out and copy the work of the “smart” student. If you’re going to have groups of students work together, then the task should really take advantage of the fact that multiple brains working together can accomplish more than those brains working in parallel but separately. In other words, you should use group worthy tasks.

Third, group work can go awry because we all have biases. The small groups in the classroom become microcosms of inequities that exist in the broader society. For example, if you have a group of three men and one woman working together, you might find that the three men ignore the contributions of the woman. Students need to learn how to work well with each other. Scan the classroom frequently for status issues (for example, by looking at each student’s body language and how much they are talking/contributing).

Finally, there is the challenge of establish and maintaining norms and expectations for group work (you have them, right?). If students aren’t familiar with your norms and expectations, you might want to find ways for students to practice working in groups before doing it in class on course content.

What other strategies do you use to ensure that active learning in your classroom supports the learning for all students? Please add your comments below.

Building Evidence Connecting Teaching Practices and More Equitable Student Outcomes (Continuously Updated)

Note: This post will be continuously updated as I gather more research on this topic.

In their paper “Active learning increases student performance in science, engineering, and mathematics,” Freeman, et al., suggest that we are seeing a new wave of “second-generation research” in the education literature that explores “which aspects of instructor behavior are most important for achieving the greatest gains with active learning, and elaborate on recent work indicating that underprepared and underrepresented students may benefit most from active methods.”

Indeed, a growing body of research shows that there are specific teaching strategies that improve learning outcomes for all students and also improve learning outcomes disproportionately for women and/or underrepresented students.

In this continuously updated blog post, I will try to maintain an annotated bibliography of such research. My goal is to provide higher education faculty and faculty developers with evidence to support teaching strategies that produce more equitable learning outcomes for all students, but particularly those who have been historically left out of STEM fields.


Huber, Bettina J., 2010. “Does Participation in Multiple High Impact Practices Affect Student Success at Cal State Northridge? Some Preliminary Insights” Northridge, CA: California State University-Northridge Office of Institutional Research.

National Survey of Student Engagement (NSSE) results from 863 graduating seniors at CSUN showed a correlation between HIP participation and higher GPA at exit and increased likelihood of graduating on time. Low-income students (Pell Grant recipients) and Latinx students had even higher GPA bump. Exit GPAs of Latinx and Pell students who didn’t participate in HIPs were lower than those of other students but if they participated in three or more HIPs their GPAs slightly exceeded other students.


Haak, D.C., HilleRisLambers, J., Pitre, E. and Freeman, S., 2011. Increased structure and active learning reduce the achievement gap in introductory biologyScience, 332(6034), pp.1213-1216.

“Highly structured” (daily and weekly practice with problem-solving, data analysis, higher-order cognitive skills) large-enrollment intro biology course for undergraduate majors at University of Washington improved learning for all students compared to low-structure (lecture intensive) version. There were disproportionately large benefits for students in their Educational Opportunity Program (many of whom are first-gen and from minority groups historically underrepresented in STEM).


Eddy, S.L. and Hogan, K.A., 2014. Getting under the hood: how and for whom does increasing course structure work?CBE-Life Sciences Education, 13(3), pp.453-468.

Essentially a replication of the 2011 study above except that the researchers studied differences between a “low structure” (lecture intensive), “moderate structure” (weekly ungraded preparatory assignments, 15-40% of each class for in-class activities on questions that were similar to previous exam problems) and “high structure” (even more prep assignments and in-class activities) for at the University of North Carolina. The same instructor taught all of the different versions of this course. Total of about 2400 students over 4 years of the study. Failure rate went down for all students in the more structured courses compared to lecture intensive version. Students also reported a greater sense of classroom community. Black students participated in the lecture intensive class far less than other students did, but in the more structured course, they spoke in class as much as other students. Exam grades improved for everyone in the moderate structure course, but it increased even more for Black students. In fact, Black students in the structured course outperformed the majority students in the lecture version of the course.And, a similar thing was observed for first-generation students.


Laursen, S.L., Hassi, M.L., Kogan, M. and Weston, T.J., 2014. Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution studyJournal for Research in Mathematics Education, 45(4), pp.406-418.

Over 3000 students across 100 different course sections in four colleges and universities were included in this study of “inquiry-based learning” (IBL) in mathematics classrooms. The students were all in a math or science major, excluding students who were preservice elementary or secondary teachers. Even though there was a range of different implementations of IBL, researchers found that students in IBL courses on average performed as well as or better than their non-IBL peers. IBL students also took as many or more math courses than non-IBL students, which seems to indicate that their interest in mathematics increased as well. Pre- and post-surveys of cognitive skills in mathematics, attitudes toward mathematics, and attitudes about collaboration in a math class. Women in non-IBL courses reported significant decreases in their confidence to pursue higher mathematics, whereas men in non-IBL courses reported an increase in their confidence. In contrast, women in IBL courses reported an increase in their confidence similar to that of men in non-IBL courses.


Winkelmes, M.A., Bernacki, M., Butler, J., Zochowski, M., Golanics, J. and Weavil, K.H., 2016. A Teaching Intervention that Increases Underserved College Students’ SuccessPeer Review18(1/2).

The researchers set out to measure the effect of teachers providing two transparently designed, problem-based take-home assignments (as compared to their original versions) on first-year college students. (“Transparently designed” here means something specific to the training that the faculty received. They were trained to revise their assignments to be clearer about the purpose, tasks, and criteria for the assignments.) About 1,180 students taught by 35 faculty, 61 courses, 7 institutions were involved in the study. Because the courses spanned many different disciplines, the researchers relied mostly on self-report data from the students. “Students who received more transparency reported gains in three areas that are important predictors of students’ success: academic confidence, sense of belonging, and mastery of the skills that employers value most when hiring.” And what’s more, for first-generation, low-income, and underrepresented students, those reported benefits were larger.


Please let me know if you encounter other research articles that provide evidence for specific teaching strategies having disproportionately positive outcomes for women and/or students historically underrepresented from STEM. I will add it to this list.

Growth Mindset and Learning about Equity, Diversity, and Inclusion

Why is it so hard for people to talk and learn about equity, diversity, and inclusion? In this post I argue that part of the answer is that many people have a fixed mindset when it comes to learning about these things.

Carol Dweck’s work on fixed and growth mindset helps to explain why people react differently to challenging situations. In broad strokes, people with a growth mindset believe that ability (as it relates to that situation) can be developed, even when one fails to overcome that challenging situation; people with a fixed mindset approach the same challenging situation with doubt about their ability to overcome the situation despite hard work and they withdraw from the situation to avoid failing.

Mindset changes over time. And, mindset can vary by domain of knowledge–in other words, my self-concept as a learner of mathematics is high and I have a growth mindset about learning mathematics but my self-concept as an athlete is low and I have a fixed mindset about learning sports. (Sidenote: it is important to remember that growth mindset is not a silver bullet–most school-based interventions involving growth mindset have been shown to yield modest effects–and that growth mindset doesn’t make up for inequities in educational opportunities in our society.)

All of us need to learn more about equity, diversity, and inclusion, especially those of us who are teachers. We need to learn about the difference between race and ethnicity, sex and gender identity. We need to learn about our own implicit biases. We need to learn about racism, sexism, ableism, and all other forms of discrimination and bias, at the personal, institutional, and societal levels.

Learning about equity, diversity, and inclusion can be scary, especially for progressive, liberal-minded folks who want to believe that we are fair and good. The thought of being labeled as a racist, sexist, *-ist person can be frightening. However, the truth is that we all carry unconscious biases that cause us to exhibit prejudice despite our best intentions. Instead of thinking of being racist as a binary state, I posit that it is more meaningful and accurate to think of ourselves as being on a journey toward ever more equitable, inclusive, and caring words and actions. We’ll never fully get there, but we still work toward that goal.

There are interesting parallels between ways that people think about learning mathematics and ways that people think about equity, diversity, and inclusion. These parallels have to do with the beliefs that people have about their abilities and the ways that they approach challenging situations. Being racist is not an innate character trait in the same way that having the ability to learn math is not a product of one’s genes.

Fixed Mindset Growth Mindset
Learning math “I’m not good at math. My sister has the math brain in the family.” (implying that there is some sort of “math gene” that they lack and that math skill is a binary trait) “I can learn math with effort and persistence.”
Learning about equity, diversity, and inclusion “I’m a good person. I’m not racist.” (denying the existence of implicit bias, and implying that being racist is a binary trait) “I can learn more about these things with effort and persistence.”
Learning math “I don’t want to attempt this mathematical task because I’m likely to fail and I don’t want to be seen as dumb.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”
Learning about equity, diversity, and inclusion “I can’t raise any controversial topics in my class because I might say the wrong thing and I don’t want to be seen as racist.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”

I draw these parallels because I suspect that appealing to growth mindset might help some educators be more willing to talk about equity, diversity, and inclusion. Many educators are already familiar with the idea of a growth mindset and actively think about how to use it in their own teaching, so they might be able to see how it also applies to learning about equity, diversity, and inclusion. Most educators I know are trying to do the right thing and aren’t overtly racist and sexist. And yet, we still need to work harder to help more folks see equity, diversity, and inclusion as central to their work.

But a growth mindset approach is not enough. For folks who train others on topics relating to equity, diversity, and inclusion, it is important to set a tone of compassion and humility. Shame and guilt often cause people to withdraw from the conversation and put up defenses.

It doesn’t help that we seem to live in an age when people’s mistakes can be captured on video and shared around the world instantly. Call-out culture makes people nervous about saying or doing the wrong thing. And, our human nature is to want to discredit a person or organization entirely once we’ve found some flaw in them/it. The pressure to be perfect is so great–I understand why some faculty want to just sit on the sidelines and avoid saying anything that could be used against them.

We desperately need to transform classrooms and schools into spaces in which instructors and students can be brave with each other and at the same time offer grace to each other when mistakes occur. Part of the solution is to establish classroom norms that foster these things. (See previous post about some possible norms to use.) Part of the solution might also be to use the growth/fixed mindset framework to help debunk myths about ourselves. I invite you to share other things that could also help in the comment section below.

The Necessity of Encouragement and Positive Feedback

According to John Gottman, professor emeritus of psychology at the University of Washington, couples in a close relationship need to have 5 times as many positive interactions than negative ones for the relationship to remain stable. Couples for whom this ratio of positive to negative interactions is less than 5 are more likely to split up compared to those whose ratio is higher than 5. Apparently, 5:1 is the “magic” ratio that strongly discriminates between couples who stay versus split.

(Side note: I’m not a psychologist, but I suspect that one reason that so many more positive interactions are required compared to negative ones is negativity bias.)

That got me thinking…is there an equivalent idea that applies to our job satisfaction as teachers and the likelihood that we will remain teachers?

We teachers receive all sorts of messages every day about our work. We receive positive ones: successes when students learn something challenging, happy smiles from students, thank you notes from family members. We receive negative ones: those lessons in which you’ve poured your heart and soul that doesn’t seem to get results, students who are rude and hostile to you, parents who don’t notice your effort, administrators that stymie your ideas, an education system that is broken, a society that doesn’t honor and value teachers.

Oh wait… I have seem to have many more negative ones than positive ones….

That year I spent teaching high school in 2009-10 was one of the hardest in my life because I received so little positive affirmation about my work as a teacher. Many of my close friends prepared me before I started teaching high school not to take mean things that students say and do personally. It took a while, but I eventually learned to do that. But still, after learning to ignore those negative messages, the positive messages were too few and far between.

Perhaps, with time I could have become a more effective high school teacher such that I could have received more positive affirmations than negative messages about my work as a teacher. But, I still strongly suspect that many of my teacher friends struggle with the brutal reality of what it means to teach in challenging situations.

So, here are some suggestions for how to invert this balance and keep ourselves sane.

Cultivate a practice of looking for successes, no matter how small. I noticed that the practice of blogging during that year of teaching helped me be more aware about the successes that I had in my teaching. I didn’t blog every day, and in retrospect, blogging more frequently could have helped. Other ideas: keeping a journal, sharing those successes with a loved one every night, meditating regularly.

Savor those positive affirmations. I keep a folder of thank you notes and other mementos. I actually do this more because I can’t bear to throw those things away, but I sometimes return to that folder on a day when I’m down on my job as a teacher. This memento has lifted me up many times.

Encourage each otherFind people around you that will support you and get in the practice of encouraging each other.

What other strategies do you employ to persist in your work as teachers? What do you think your positive/negative ratio is right now and where do you think it should be for you to feel good about your work? I’d love to hear your comments.

 

 

Growth is Uncomfortable

Today, in our Claremont Colleges Center for Teaching and Learning Book Club meeting, my colleague Kathy Van Heuvelen shared with us a great analogy relating to the current controversy about “safe spaces” in college classrooms: Good athletes know their bodies well enough to know the difference between soreness and injury. Soreness is a sign that you’ve been working your body hard and that you’re getting stronger and faster. Injury is a sign that you’ve gone too far and need healing.

In a similar vein, our job as instructors is to help students develop the self-awareness to know the difference between feeling uncomfortable with having our ideas and beliefs challenged (a sign that we’re on our way to getting stronger and wiser) and feeling alienated, marginalized, or belittled. I posit that “brave spaces” are classroom environments in which students expect the former and not the latter.

I firmly believe that a good college education should challenge students with ideas and beliefs that are different from their own and should help them to develop the reflective judgment and skills of inquiry to be able to think on their own.

There is a lot of misunderstanding in the popular media about “safe spaces”. I fully agree that we don’t want spaces in which students never encounter any ideas that they find challenging or uncomfortable. I want students to encounter feel challenged (and perhaps even desire it), but in an environment where there is discomfort within a structure that gives them a sense of security. The kind of “safe spaces” that are being described in the media sound like echo chambers where you only hear your own thoughts, and no colleague that I have talked to wants that for our students either.

 

Some probability problems for your consideration

As I was preparing this tweet on AMS prizes given at the 2016 Joint Mathematics Meetings…

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…I checked the AMS Annual Survey of the Mathematical Sciences to determine that in 2015 roughly 30% of full-time faculty in the mathematical sciences were female. Then, I wrote and did the following math problem:

Question #1: Suppose that 20 people are being chosen for various awards. Assume that for each award, there is a committee that narrows the field of candidates down to a set of 10 finalists who are deserving of the award, and 3 of them are female. Assume that each committee independently chooses the winner from this set of finalists in such a way that each of the finalists is equally likely to win the award. What is the probability that none of the 20 people are women?

Answer: (0.7)^20 ≈ 0.0007979

That seems really unlikely.

Some people are going to argue that because women have been excluded from the mathematical sciences to a greater degree in our recent history, the population of senior people who have made big contributions to their fields is going to skew even more male than the general population of full-time faculty.  (BTW, not all of the awards above are for senior people who’ve made big contributions.) OK, so let’s consider another problem.

Question #2: Keep everything from Question #1 the same but this time let’s assume that x (in %) of the finalists for each award are men. What would x have to be so that the probability of not having any women chosen is something more likely, like 25%?

Answer: x^20=0.25 means x ≈ .933 ( or 93.3%)

Is it the case that there are so few women deserving of awards in mathematics?

I assert that we don’t suffer from a lack of talented women and people of color in the mathematical sciences. The problem is that we don’t nurture talented women and people of color, don’t recognize their talent, and don’t take enough steps to make sure our award processes are unbiased, fair, and equitable. (There is plenty of evidence that women are just as implicitly biased against women as men are.)

Look at the dramatic change in the representation of people of color in this year’s Oscar nominations, compared to a mere two years ago when #OscarsSoWhite was trending. Did the field suddenly produce a bunch of new Black artists and producers and directors in those two years? No.  So why can’t those of us in the mathematical sciences also try harder to make sure that we make sure award winners are more broadly representative?

Every time a women or person of color looks at a list of winners like this one, they receive messages that they aren’t welcome in the field.

Important caveats:

  • These two problems are just food for thought. I’m not implying that the actual awarding of the AMS prizes is anything like what is described above.
  • I’m not suggesting that any of the selection committee members were deliberately being racist or sexist.
  • I’m not suggesting that any of the winners of the awards were not deserving and should return their prizes.
  • Also, my tweet and this post is about the underrepresentation of women, and I also recognize that there is an underrepresentation of African-American, Hispanic/Latinx, and Native American people among the award winners.

It would be interesting to go back in history to look at the demographics of all AMS prize winners.

Recommended reading:

Addressing the underrepresentation of women in mathematics conferences” by Greg Martin

The MAA’s guidelines for award selection committees on how to avoid implicit bias.